Feynman path integrals for magnetic Schrödinger operators on infinite weighted graphs

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We prove a Feynman path integral formula for the unitary group exp(—itLυ,θ), t ≥ 0, associated with a discrete magnetic Schrodinger operator Lυ,θ on a large class of weighted infinite graphs. As a consequence, we get a new Kato-Simon estimate $$\left| {\exp \left({- it{L_{v,\theta}}} \right)\left({x,y} \right)} \right| \le \exp \left({- t{L_{- \deg ,0}}} \right)\left({x,y} \right),$$ which controls the unitary group uniformly in the potentials in terms of a Schrodinger semigroup, where the potential deg is the weighted degree function of the graph.